A digital to analog (D/A) converter is a device that generates an analog voltage signal in response to its digital representation. Typically, the accuracy of a state-of-the-art D/A converter is related to the resolution of the digital signal representation. For example, an 8-bit D/A converter generates up to 256 different discrete voltage values to recreate the signal and, therefore, the accuracy to reproduce each of these voltage values is sufficient to provide approximately equal increments between contiguous voltage values, about ±one half increment, or in this example, about ±0.2% of the full scale. But for applications involving integration, such as in the control of inertial sensors, accelerometers and gyroscopes, the analog accuracy and stability is much more important than the resolution. Because of this, D/A converters using pulse width modulation are well suited for these applications.
However, the accuracy of the state of the art D/A converters using pulse width modulation is affected by numerous factors resulting in errors. For example, the response of the state of the art D/A converters is inherently non-linear caused by the resistance imbalance in the switching device of the converter. Even if an initial resistance imbalance is removed by factory adjustment, a resistance imbalance typically appears in time as a result of aging and, particularly in space applications, of radiation. Such non-linearity in the response results in errors of several PPM's. Another source of error is the high sensitivity to the reference voltages and to propagation delays in D/A converters using pulse width modulation to switch between two reference voltages equal in value but of opposite polarities. The errors of each reference voltages, drifts and mismatch, combine to create errors in the output. Propagation delay errors that affect the duty cycle have full impact on the accuracy of the output. When the output voltage is small, these errors will appear that much greater in relative terms. To reduce these sensitivities and increase the accuracy a 2 bit digital signal is used to provide two pulse width modulations instead of just one to switch between zero volt and one of the reference voltages, either positive or negative depending on the polarity of the voltage to be created. This is much more accurate especially for small near zero output voltages. A new source of error arises from this, albeit less serious than the problem this double modulation seeks to reduce. This other source of error is cross-over discontinuity. At every switching operation there is a small difference of propagation time delay between the time the switches respond to a turn ON command and the time it responds to a turn OFF command resulting in a pulse deficit or excess which is constant for each modulation or polarity but differs from one polarity to the other. The differing pulse deficits/excesses for different polarities result in so-called cross-over discontinuity in the averaged signal when passing from one polarity to the other, substantially affecting the accuracy of the filtered signal. Yet another source of error voltage drift normally associated with the use of an operational amplifier in the low-pass filter.
However, for certain applications such as the control of gyroscopes and accelerometers in space applications it is necessary to employ a D/A converter that offers a relatively fast response and a very accurate response over a longer period of use.
It would be advantageous to provide a very accurate D/A converter that overcomes some of the known drawbacks of the prior art through circuit design using parts that are readily available in radiation hardened versions.
It is, therefore, an object of the invention to provide a D/A converter based on a circuit design that overcomes the drawbacks of the prior art using parts that are readily available in radiation hardened versions.
It is further an object of the invention to provide a modulation scheme for eliminating cross-over discontinuity when passing from one polarity to the other.